1. to thrust at someone (e.g. a weapon); to point (a gun, knife, etc.) at; to hold up threateningly to (someone's face)
男が、こちらに銃を突きつける。The man points a gun at us.
2. to present forcefully (demand, document, etc.); to confront someone with (evidence, facts, etc.); to force upon
よくわからない要求を突きつけられた。I was confronted with a demand I didn't really understand.